def pdsolve(eq,
func=None,
hint='default',
dict=False,
solvefun=None,
**kwargs):
"""
Solves any (supported) kind of partial differential equation.
**Usage**
pdsolve(eq, f(x,y), hint) -> Solve partial differential equation
eq for function f(x,y), using method hint.
**Details**
``eq`` can be any supported partial differential equation (see
the pde docstring for supported methods). This can either
be an Equality, or an expression, which is assumed to be
equal to 0.
``f(x,y)`` is a function of two variables whose derivatives in that
variable make up the partial differential equation. In many
cases it is not necessary to provide this; it will be autodetected
(and an error raised if it couldn't be detected).
``hint`` is the solving method that you want pdsolve to use. Use
classify_pde(eq, f(x,y)) to get all of the possible hints for
a PDE. The default hint, 'default', will use whatever hint
is returned first by classify_pde(). See Hints below for
more options that you can use for hint.
``solvefun`` is the convention used for arbitrary functions returned
by the PDE solver. If not set by the user, it is set by default
to be F.
**Hints**
Aside from the various solving methods, there are also some
meta-hints that you can pass to pdsolve():
"default":
This uses whatever hint is returned first by
classify_pde(). This is the default argument to
pdsolve().
See also the classify_pde() docstring for more info on hints,
and the pde docstring for a list of all supported hints.
**Tips**
- You can declare the derivative of an unknown function this way:
>>> from sympy import Function, Derivative
>>> from sympy.abc import x, y # x and y are the independent variables
>>> f = Function("f")(x, y) # f is a function of x and y
>>> # fx will be the partial derivative of f with respect to x
>>> fx = Derivative(f, x)
>>> # fy will be the partial derivative of f with respect to y
>>> fy = Derivative(f, y)
- See test_pde.py for many tests, which serves also as a set of
examples for how to use pdsolve().
- pdsolve always returns an Equality class (except for the case
when the hint is "all" or "all_Integral"). Note that it is not possible
to get an explicit solution for f(x, y) as in the case of ODE's
- Do help(pde.pde_hintname) to get help more information on a
specific hint
Examples
========
>>> from sympy.solvers.pde import pdsolve
>>> from sympy import Function, diff, Eq
>>> from sympy.abc import x, y
>>> f = Function('f')
>>> u = f(x, y)
>>> ux = u.diff(x)
>>> uy = u.diff(y)
>>> eq = Eq(1 + (2*(ux/u)) + (3*(uy/u)))
>>> pdsolve(eq)
f(x, y) == F(3*x - 2*y)*exp(-2*x/13 - 3*y/13)
"""
given_hint = hint # hint given by the user.
if not solvefun:
solvefun = Function('F')
# See the docstring of _desolve for more details.
hints = _desolve(eq,
func=func,
hint=hint,
simplify=True,
type='pde',
**kwargs)
all_ = hints.pop('all', False)
if all_:
raise NotImplementedError("Only one hint has been added till now")
else:
solvefunc = globals()['pde_' + hints[hint]]
return solvefunc(eq, hints['func'], hints['order'],
hints[hints['hint']], solvefun)
def pdsolve(eq, func=None, hint='default', dict=False, solvefun=None, **kwargs):
"""
Solves any (supported) kind of partial differential equation.
**Usage**
pdsolve(eq, f(x,y), hint) -> Solve partial differential equation
eq for function f(x,y), using method hint.
**Details**
``eq`` can be any supported partial differential equation (see
the pde docstring for supported methods). This can either
be an Equality, or an expression, which is assumed to be
equal to 0.
``f(x,y)`` is a function of two variables whose derivatives in that
variable make up the partial differential equation. In many
cases it is not necessary to provide this; it will be autodetected
(and an error raised if it couldn't be detected).
``hint`` is the solving method that you want pdsolve to use. Use
classify_pde(eq, f(x,y)) to get all of the possible hints for
a PDE. The default hint, 'default', will use whatever hint
is returned first by classify_pde(). See Hints below for
more options that you can use for hint.
``solvefun`` is the convention used for arbitrary functions returned
by the PDE solver. If not set by the user, it is set by default
to be F.
**Hints**
Aside from the various solving methods, there are also some
meta-hints that you can pass to pdsolve():
"default":
This uses whatever hint is returned first by
classify_pde(). This is the default argument to
pdsolve().
"all":
To make pdsolve apply all relevant classification hints,
use pdsolve(PDE, func, hint="all"). This will return a
dictionary of hint:solution terms. If a hint causes
pdsolve to raise the NotImplementedError, value of that
hint's key will be the exception object raised. The
dictionary will also include some special keys:
- order: The order of the PDE. See also ode_order() in
deutils.py
- default: The solution that would be returned by
default. This is the one produced by the hint that
appears first in the tuple returned by classify_pde().
"all_Integral":
This is the same as "all", except if a hint also has a
corresponding "_Integral" hint, it only returns the
"_Integral" hint. This is useful if "all" causes
pdsolve() to hang because of a difficult or impossible
integral. This meta-hint will also be much faster than
"all", because integrate() is an expensive routine.
See also the classify_pde() docstring for more info on hints,
and the pde docstring for a list of all supported hints.
**Tips**
- You can declare the derivative of an unknown function this way:
>>> from sympy import Function, Derivative
>>> from sympy.abc import x, y # x and y are the independent variables
>>> f = Function("f")(x, y) # f is a function of x and y
>>> # fx will be the partial derivative of f with respect to x
>>> fx = Derivative(f, x)
>>> # fy will be the partial derivative of f with respect to y
>>> fy = Derivative(f, y)
- See test_pde.py for many tests, which serves also as a set of
examples for how to use pdsolve().
- pdsolve always returns an Equality class (except for the case
when the hint is "all" or "all_Integral"). Note that it is not possible
to get an explicit solution for f(x, y) as in the case of ODE's
- Do help(pde.pde_hintname) to get help more information on a
specific hint
Examples
========
>>> from sympy.solvers.pde import pdsolve
>>> from sympy import Function, diff, Eq
>>> from sympy.abc import x, y
>>> f = Function('f')
>>> u = f(x, y)
>>> ux = u.diff(x)
>>> uy = u.diff(y)
>>> eq = Eq(1 + (2*(ux/u)) + (3*(uy/u)))
>>> pdsolve(eq)
f(x, y) == F(3*x - 2*y)*exp(-2*x/13 - 3*y/13)
"""
given_hint = hint # hint given by the user.
if not solvefun:
solvefun = Function('F')
# See the docstring of _desolve for more details.
hints = _desolve(eq, func=func,
hint=hint, simplify=True, type='pde', **kwargs)
eq = hints.pop('eq', False)
all_ = hints.pop('all', False)
if all_:
# TODO : 'best' hint should be implemented when adequate
# number of hints are added.
pdedict = {}
failed_hints = {}
gethints = classify_pde(eq, dict=True)
pdedict.update({'order': gethints['order'],
'default': gethints['default']})
for hint in hints:
try:
rv = _helper_simplify(eq, hint, hints[hint]['func'],
hints[hint]['order'], hints[hint][hint], solvefun)
except NotImplementedError as detail:
failed_hints[hint] = detail
else:
pdedict[hint] = rv
pdedict.update(failed_hints)
return pdedict
else:
return _helper_simplify(eq, hints['hint'],
hints['func'], hints['order'], hints[hints['hint']], solvefun)
def pdsolve(eq, func=None, hint='default', dict=False, solvefun=None, **kwargs):
"""
Solves any (supported) kind of partial differential equation.
**Usage**
pdsolve(eq, f(x,y), hint) -> Solve partial differential equation
eq for function f(x,y), using method hint.
**Details**
``eq`` can be any supported partial differential equation (see
the pde docstring for supported methods). This can either
be an Equality, or an expression, which is assumed to be
equal to 0.
``f(x,y)`` is a function of two variables whose derivatives in that
variable make up the partial differential equation. In many
cases it is not necessary to provide this; it will be autodetected
(and an error raised if it couldn't be detected).
``hint`` is the solving method that you want pdsolve to use. Use
classify_pde(eq, f(x,y)) to get all of the possible hints for
a PDE. The default hint, 'default', will use whatever hint
is returned first by classify_pde(). See Hints below for
more options that you can use for hint.
``solvefun`` is the convention used for arbitrary functions returned
by the PDE solver. If not set by the user, it is set by default
to be F.
**Hints**
Aside from the various solving methods, there are also some
meta-hints that you can pass to pdsolve():
"default":
This uses whatever hint is returned first by
classify_pde(). This is the default argument to
pdsolve().
See also the classify_pde() docstring for more info on hints,
and the pde docstring for a list of all supported hints.
**Tips**
- You can declare the derivative of an unknown function this way:
>>> from sympy import Function, Derivative
>>> from sympy.abc import x, y # x and y are the independent variables
>>> f = Function("f")(x, y) # f is a function of x and y
>>> # fx will be the partial derivative of f with respect to x
>>> fx = Derivative(f, x)
>>> # fy will be the partial derivative of f with respect to y
>>> fy = Derivative(f, y)
- See test_pde.py for many tests, which serves also as a set of
examples for how to use pdsolve().
- pdsolve always returns an Equality class (except for the case
when the hint is "all" or "all_Integral"). Note that it is not possible
to get an explicit solution for f(x, y) as in the case of ODE's
- Do help(pde.pde_hintname) to get help more information on a
specific hint
Examples
========
>>> from sympy.solvers.pde import pdsolve
>>> from sympy import Function, diff, Eq
>>> from sympy.abc import x, y
>>> f = Function('f')
>>> u = f(x, y)
>>> ux = u.diff(x)
>>> uy = u.diff(y)
>>> eq = Eq(1 + (2*(ux/u)) + (3*(uy/u)))
>>> pdsolve(eq)
f(x, y) == F(3*x - 2*y)*exp(-2*x/13 - 3*y/13)
"""
given_hint = hint # hint given by the user.
if not solvefun:
solvefun = Function('F')
# See the docstring of _desolve for more details.
hints = _desolve(eq, func=func,
hint=hint, simplify=True, type='pde', **kwargs)
eq = hints['eq']
all_ = hints.pop('all', False)
if all_:
raise NotImplementedError("Only one hint has been added till now")
else:
solvefunc = globals()['pde_' + hints[hint]]
return solvefunc(eq, hints['func'], hints['order'], hints[hints['hint']],
solvefun)
